The population (in thousands) of a colony of bacteria t minutes after the introduction of a toxin is given by the function

P(t)= (piecewise) t^2+1 if 0(greater than or equal to)t

Question

The population (in thousands) of a colony of bacteria t minutes after the introduction of a toxin is given by the function 

P(t)= (piecewise) t^2+1 if 0(greater than or equal to)t<5
-8t+66 if t is greater than or equal to 5

a. When does the colony die out?
b. Show that at some time between t=2 and t=7, the population is 9,000

The topic of the section is continuity. I just don't get how to do it properly
for a I set the second equation to 0 and solved for t and got 8.25 seconds. Is that the right way to do it? 
I cant figure out part b though

anonymous · Answer

I just did part b by setting them both to 9 and choosing the answer that was in the (2,7)
so t^2+1=9= t=2.83 rounded up, is that right?